Related papers: Stochastic Modelling in Fluid Dynamics: It\^o vs S…

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The Legendre transform of the Lagrangian formulation of these SPDEs yields their Lie-Poisson Hamiltonian…

In this work we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble…

Interpreting the noise in a stochastic differential equation, in particular the It\^o versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of…

The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral,…

The purpose of this paper is to examine the Lagrangian stochastic modeling of the fluid velocity seen by inertial particles in a nonhomogeneous turbulent flow. A new Langevin-type model, compatible with the transport equation of the drift…

Stochastic modelling necessitates an interpretation of noise. In this paper, we describe the loss of deterministically stable behaviour in a fundamental fluid mechanics problem, conditional to whether noise is introduced in the sense of…

Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…

The It\^{o} and Stratonovich approaches are two ways to integrate stochastic differential equations. Detailed knowledge of the origin of the stochastic noise is needed to determine which approach suits a particular problem. I discuss this…

In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…

It is widely assumed that there exists a simple transformation from the It\^o interpretation to the one by Stratonovich and back for any stochastic differential equation of applied interest. While this transformation exists under suitable…

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…

This paper compares the results of applying a recently developed method of stochastic uncertainty quantification designed for fluid dynamics to the Born-Infeld model of nonlinear electromagnetism. The similarities in the results are…

We construct sub-grid scale models of incompressible fluids by considering expectations of semi-martingale Lagrangian particle trajectories. Our construction is based on the Lagrangian decomposition of flow maps into mean and fluctuation…

We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develop a stochastic Clebsch action principle, in which the noise…

We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…

The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…

In this work, a stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the large-scale oceanic circulation. This stochastic framework arises from a decomposition of the…

Langevin equation with a multiplicative stochastic force is considered. That force is uncorrelated, it has the L\'evy distribution and the power-law intensity. The Fokker-Planck equations, which correspond both to the It\^o and Stratonovich…

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of…